On a class of linear operators.
On a Kleinecke-Shirokov theorem
We prove that for normal operators the generalized commutator approaches zero when tends to zero in the norm of the Schatten-von Neumann class with and varies in a bounded set of such a class.
On a weighted Toeplitz operator and its commutant.
On bounded Dual-valued derivations on certain Banach algebras
On certain classes of commutators.
On Commuting Unbounded Self-Adjoint Operators. III.
On continuity of linear transformations commuting with generalized scalar operators (Preliminary communication)
On derivations and crossed homomorphisms
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...
On derivations over rings of triangular matrices
On functional inequalities originating from module Jordan left derivations.
On generalized derivations in Banach algebras
We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ A. In particular, we show that if A is unital and semisimple, then G is inner and implemented by elements of the socle of A.
On innerness of derivations on .
On Intertwining Operators.
On Jordan *-derivations and an application
On Minimizing ||S−(AX−XB)||Pp
In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp , where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.
On minimizing the norm of linear maps in -classes.
On Quasi-Normality of Two-Sided Multiplication
2000 Mathematics Subject Classification: 47B47, 47B10, 47A30.In this note, we characterize quasi-normality of two-sided multiplication, restricted to a norm ideal and we extend this result, to an important class which contains all quasi-normal operators. Also we give some applications of this result.
On the Kleinecke-Shirokov Theorem for families of derivations
It is proved that Riesz elements in the intersection of the kernel and the closure of the image of a family of derivations on a Banach algebra are quasinilpotent. Some related results are obtained.
On the Putnam--Fuglede theorem.
On the Range and the Kernel of Derivations
2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.Let H be a separable infinite dimensional complex Hilbert space and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A ∈ L(H), the derivation δA : L(H)→ L(H) is defined by δA(X) = AX-XA. In this paper we prove that if A is an n-multicyclic hyponormal operator and T is hyponormal such that AT = TA, then || δA(X)+T|| ≥ ||T|| for all X ∈ L(H). We establish the same inequality if A is...